rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Tensor Categories and Endomorphisms of von Neumann Algebras
    sub title: with Applications to Quantum Field Theory
  name:
    name part: Bischoff, Marcel.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Kawahigashi, Yasuyuki.
    role:
      role term: author.
  name:
    name part: Longo, Roberto.
    role:
      role term: author.
  name:
    name part: Rehren, Karl-Henning.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2015
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: X, 94 p. 138 illus. online resource.
  abstract: C* tensor categories are a point of contact where Operator Algebras and Quantum Field Theory meet. They are the underlying unifying concept for homomorphisms of (properly infinite) von Neumann algebras and representations of quantum observables. The present introductory text reviews the basic notions and their cross-relations in different contexts. The focus is on Q-systems that serve as complete invariants, both for subfactors and for extensions of quantum field theory models. It proceeds with various operations on Q-systems (several decompositions, the mirror Q-system, braided product, centre and full centre of Q-systems) some of which are defined only in the presence of a braiding. The last chapter gives a brief exposition of the relevance of the mathematical structures presented in the main body for applications in Quantum Field Theory (in particular two-dimensional Conformal Field Theory, also with boundaries or defects).
  table of contents: Introduction -- Homomorphisms of von Neumann algebras -- Endomorphisms of infinite factors -- Homomorphisms and subfactors -- Non-factorial extensions -- Frobenius algebras, Q-systems and modules -- C* Frobenius algebras -- Q-systems and extensions -- The canonical Q-system -- Modules of Q-systems -- Induced Q-systems and Morita equivalence -- Bimodules -- Tensor product of bimodules -- Q-system calculus -- Reduced Q-systems -- Central decomposition of Q-systems -- Irreducible decomposition of Q-systems -- Intermediate Q-systems -- Q-systems in braided tensor categories -- a-induction -- Mirror Q-systems -- Centre of Q-systems -- Braided product of Q-systems -- The full centre -- Modular tensor categories -- The braided product of two full centres -- Applications in QFT -- Basics of algebraic quantum field theory -- Hard boundaries -- Transparent boundaries -- Further directions -- Conclusions.
  note: by Marcel Bischoff, Yasuyuki Kawahigashi, Roberto Longo, Karl-Henning Rehren.
  subject:
    topic: Physics
  subject:
    topic: Algebra
  subject:
    topic: Mathematical physics
  subject:
    topic: Quantum field theory
  subject:
    topic: String theory
  subject:
    topic: Physics
  subject:
    topic: Quantum Field Theories, String Theory
  subject:
    topic: Mathematical Physics
  subject:
    topic: Algebra
  classification: QC174.45-174.52
  classification: 530.14
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: SpringerBriefs in Mathematical Physics, 3
  identifier: 9783319143019
  identifier: http://dx.doi.org/10.1007/978-3-319-14301-9
  record info:
    record creation date: 150113
    record change date: 20151106151046.0
    record identifier: 978-3-319-14301-9